Q. No.The equation of vibration of a taut string, fixed at both ends, is given by; \(y=(3~\text{mm})~\text{cos}\left(\dfrac{\pi x}{10~\text{cm}}\right)~\text{sin}(800\pi~\text{s}^{-1}{t}).\) The positions of the nodes are:
1.
\(x= 0~\text{cm}, 10~\text{cm}, 20~\text{cm},....\)
2.
\(x= 0~\text{cm}, 20~\text{cm}, 40~\text{cm},....\)
3.
\(x= 5~\text{cm}, 10~\text{cm}, 15~\text{cm},....\)
4.
\(x= 5~\text{cm}, 15~\text{cm}, 25~\text{cm},....\)
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1. \(A\)
2. \(\sqrt 2A\)
3. \(2A\)
4. \((2+\sqrt2)A\)
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| 1. | \(1\) | 2. | \(1/2\) |
| 3. | \(2/3\) | 4. | \(3/2\) |
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| 1. | its internal energy |
| 2. | its internal energy per unit volume |
| 3. | its internal energy per unit mass |
| 4. | its internal energy per unit temperature |
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1. \(\dfrac{ 1}{2L} \sqrt {\dfrac{T}{m}}\)
2. \(\dfrac{1}{4 L} \sqrt{\dfrac{T}{m}}\)
3. \(\dfrac{1}{2} \sqrt{\dfrac{TL}{2m}}\)
4. \(\dfrac{1}{2} \sqrt{\dfrac{T}{m L}}\)
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| 1. | \(2^{\text{nd}}\) harmonic | 2. | \(3^{\text{rd}}\) harmonic |
| 3. | \(6^{\text{th}}\) harmonic | 4. | \(12^{\text{th}}\) harmonic |
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At which points is the amplitude equal to \(2\) mm?
| 1. | \(x = \) \(10\) cm, \(20\) cm, \(30\) cm, \(40\) cm |
| 2. | \(x=\) \(10\) cm, \(15\) cm, \(30\) cm, \(45\) cm |
| 3. | \(x =\) \(10\) cm, \(20\) cm, \(40\) cm, \(80\) cm |
| 4. | \(x = \) \(10\) cm, \(20\) cm, \(40\) cm, \(50\) cm |
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is superposed with another waveform \(y=4A\cos(\omega t-kx).\) The amplitude of the resulting waveform will be:
| 1. | \(7A\) | 2. | \(A\) |
| 3. | \(3.5A\) | 4. | \(5A\) |
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| Statement I: | Sound waves travelling from air into water, incident obliquely, bend towards the normal. |
| Statement II: | Sound waves travel more slowly in water than in air. |
| 1. | Statement I is incorrect and Statement II is correct. |
| 2. | Both Statement I and Statement II are correct. |
| 3. | Both Statement I and Statement II are incorrect. |
| 4. | Statement I is correct and Statement II is incorrect. |
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| Statement I: | The speed of sound waves in a medium depends on the elastic modulus and the density of the medium. |
| Statement II: | The speed of sound in a gas is independent of its temperature. |
| 1. | Statement I is incorrect and Statement II is correct. |
| 2. | Both Statement I and Statement II are correct. |
| 3. | Both Statement I and Statement II are incorrect. |
| 4. | Statement I is correct and Statement II is incorrect. |
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